3. Complexity (Arecchi, 1996, 1999a)
The logical construction of the world starting from its elements leads to simple results only in particular cases. In general the procedure yields a tree of possible solutions with many branches, the number of which increases exponentially with the size of the system, that is, with the number of the elementary components. Characterizing all possible final states of such a dynamics, would be an “intractable” task, since the corresponding computation time is generally longer than the effective time necessary to the piece of world under investigation to reach a final state. In such a case the most sensible thing is to sit down and wait until things happen, giving up with predictability. Of course, this would be highly unsatisfactory since it would mean recognizing the failure of the scientific program.
Considering the computation time shifts the emphasis from the “problem solving” to the “decision making”. Ideally, one could solve a problem in an extremely long time. But in real life, every agent is embedded in a changing world and his vital decisions, such as adaptation to the environment, defence from a danger, classification of the phenomena, must be taken while the world is changing, thus they are relevant only if the decision time is shorter than the correlation time of the outside connotations.
Before offering a remedy, that I will call “adaptive strategy”, and which is equivalent to re-introducing the classical criterion of truth as “adaequatio”, let me explain how the problem of complexity has risen within the scientific program.
The words of the ordinary language are polysemous since they do not refer to isolated objects but to objects embedded in a context. No object can be isolated from its context, since its interaction with the environment contributes to assigning different nuances. If we call “event” an object plus its context, the same word denotes, in a rather ambiguous way, a whole collection of events. This collection represents the semantic space of that word. In a historical dictionary the set of all possible meanings is truncated to a finite small number of connotations, that is, those used by the Authors in the literature of that language.
A text, seen as a flow of words connected by grammatical rules, appears as a wide riverbed which joins different semantic spaces. Within it, one can cut different interpretations. As well known, no text can be read in a univocal way and in order to reduce the range of possible interpretations, we need to consider elements outside the text. A self consistent reading of a text, whereby each word is specified by its correlation with the other ones, it rather illusory.
We call complexity the fact that the global information (I here use information in the common sense without referring to a technical meaning) is not the sum of each information that the dictionary attributes to each word; in fact there is a mutual information emerging from the structure of the literary text and from the semantic memory recalled by the used terms.
All the above ambiguities seemed overcome by Galileo’s program. Limiting the attention to quantities is equivalent to applying a measuring apparatus M with a protocol of use. The output number from M is a suitable coding of a specific quantity, and it is unique. The words – numbers are connected by a new grammar which is mathematics and which – at least at the time of Galileo – provides connections without ambiguity. Thus science is built by univocal terms connected by necessary rules. Once a sufficient number of initial observations establishes a set of terms and of their connections (the natural “laws”) one can extract all consequences by deduction, thus anticipating events before they occur. This is the predictability of science, a virtue absent in the ordinary language.
